from quantum physics to expand into general pop culture.

拓展到普羅大眾文化的物理原理之一

It says that you can never simultaneously know the exact position

它指出我們無法既確定一個物體的位置

and the exact speed of an object and shows up as a metaphor in everything

又同時精準測得這它的速率。 這在許多領域被當成隱喻使用

from literary criticism to sports commentary.

從藝文評論到體育播報領域都有

Uncertainty is often explained as a result of measurement,

測不準原理常常被認為源自於測量行為

that the act of measuring an object's position changes its speed, or vice versa.

測量物體位置的動作 同時會改變其速度，反之亦然

The real origin is much deeper and more amazing.

但是真正的原理更加深奧 也更加驚奇有趣

The Uncertainty Principle exists because everything in the universe

之所以會有測不準原理 是因為宇宙中的任何東西

behaves like both a particle and a wave at the same time.

都同時兼具「粒子」和「波」的兩種性質

In quantum mechanics, the exact position and exact speed of an object

在量子力學中，一個物體的 確切位置和速度是沒有意義的

have no meaning.

為了理解它

To understand this,

我們需要釐清一下： 表現得像「粒子」或像「波」的含意

we need to think about what it means to behave like a particle or a wave.

粒子可在某一時間存在於特定位置

Particles, by definition, exist in a single place at any instant in time.

我們能利用在特定位置 發現此物體的機率圖形

We can represent this by a graph showing the probability of finding

來呈現這個定義 圖形上會有一個高峰值

the object at a particular place, which looks like a spike,

物體在某個特定位置 出現的機率是 100%，在他處則都是 0%

100% at one specific position, and zero everywhere else.

而波則是「擾動」在空間中傳播的現象

Waves, on the other hand, are disturbances spread out in space,

就像是湖面上的漣漪

like ripples covering the surface of a pond.

我們可將「波」視為整體 然後確認其性質

We can clearly identify features of the wave pattern as a whole,

其中最重要的就是波長

most importantly, its wavelength,

波長是相鄰兩個波峰或波谷之間的距離

which is the distance between two neighboring peaks,

但是我們無法確認波的位置

or two neighboring valleys.

波在各種不同的位置出現的機率都很大

But we can't assign it a single position.

波長在量子物理學不可或缺的

It has a good probability of being in lots of different places.

因為物體的(物質波)波長與其動量有關

Wavelength is essential for quantum physics

動量 = 質量 Χ 速度

because an object's wavelength is related to its momentum,

一個快速運動的物體具有很大的動量

mass times velocity.

伴隨著波長很短的物質波

A fast-moving object has lots of momentum,

很重的物體即使動得不快 仍具有很大的動量

which corresponds to a very short wavelength.

同樣的，也代表了它的波長很短

A heavy object has lots of momentum even if it's not moving very fast,

這就是我們無法察覺 日常物體波動性質的原因

which again means a very short wavelength.

如果你丟出一個棒球

This is why we don't notice the wave nature of everyday objects.

它的波長是1公尺的10的33次方之一

If you toss a baseball up in the air,

因為實在是太小了，所以不可能被測到

its wavelength is a billionth of a trillionth of a trillionth of a meter,

但微小的物體，例如原子或電子束

far too tiny to ever detect.

波長就大到足以用物理實驗量測出來

Small things, like atoms or electrons though,

如果我們有一個純粹的波 就可以測量它的波長

can have wavelengths big enough to measure in physics experiments.

進而算出它的動量 但是卻無法測出它的確實位置

So, if we have a pure wave, we can measure its wavelength,

另一方面，我們很容易確知粒子的位置

and thus its momentum, but it has no position.

但它卻並沒有波長 所以我們不知道它的動量大小

We can know a particles position very well,

為了同時得到 一個粒子的位置與動量

but it doesn't have a wavelength, so we don't know its momentum.

我們需要融合兩種圖像

To get a particle with both position and momentum,

創造一個侷限 在很小區域的波圖像

we need to mix the two pictures

那該如何進行呢？

to make a graph that has waves, but only in a small area.

方法是：藉由疊加數個不同波長的的波

How can we do this?

因為一個波一種動量 這代表賦予物體具備不同動量的可能性

By combining waves with different wavelengths,

當我們將兩個波疊加起來時

which means giving our quantum object some possibility of having different momenta.

波峰對齊的地方會形成更高的波峰

When we add two waves, we find that there are places

在另外一些位置 因波峰與波谷對齊而相互抵銷

where the peaks line up, making a bigger wave,

結果就是有些地方我們看得到波

and other places where the peaks of one fill in the valleys of the other.

另一些地方，則什麼都沒有

The result has regions where we see waves

如果我們再加上第三個波

separated by regions of nothing at all.

那些波被抵銷的區域變大了

If we add a third wave,

加上第四個，持續變大 而有波的區域逐漸變窄

the regions where the waves cancel out get bigger,

如果我們持續疊加更多的波 就能得到一個波包

a fourth and they get bigger still, with the wavier regions becoming narrower.

在一個很小的區域內有一個確定的波長

If we keep adding waves, we can make a wave packet

這就得到了一個 同時擁有波與粒子屬性的物體

with a clear wavelength in one small region.

但是這樣一來 位置和動量都無法準確測得

That's a quantum object with both wave and particle nature,

物體並非侷限在一個單一位置上

but to accomplish this, we had to lose certainty

在波包內的範圍裡 我們發現物體的機率都很高

about both position and momentum.

我們透過疊加多個波得到波包

The positions isn't restricted to a single point.

意味著我們就有可能找到 與其中一個物體相對應的動量

There's a good probability of finding it within some range

導致位置與動量都無法精確測量

of the center of the wave packet,

這都與測不準原理有關

and we made the wave packet by adding lots of waves,

如果你想更精確的測量位置

which means there's some probability of finding it

就得用更多的波疊加起來， 加以建造出更小的波包

with the momentum corresponding to any one of those.

波數增加使動量更不確定

Both position and momentum are now uncertain,

如果你想更明確的得到動量值 就需要一個更大的波包

and the uncertainties are connected.

結果位置就更不確定

If you want to reduce the position uncertainty

這就是海森堡測不準原理

by making a smaller wave packet, you need to add more waves,

最初由德國物理學家 Werner Heisenberg 於1927 年提出

which means a bigger momentum uncertainty.

這種測不準的特性與測量的精確度無關

If you want to know the momentum better, you need a bigger wave packet,

是結合波和粒子 兩種性質之後不可避免的結果

which means a bigger position uncertainty.

測不準原理不僅僅 是測量上的實際限制

That's the Heisenberg Uncertainty Principle,

它是物體只能表現出 一種(波或粒子)性質的限制

first stated by German physicist Werner Heisenberg back in 1927.

已被建入宇宙基本構造之中

This uncertainty isn't a matter of measuring well or badly,

but an inevitable result of combining particle and wave nature.

The Uncertainty Principle isn't just a practical limit on measurment.

It's a limit on what properties an object can have,

built into the fundamental structure of the universe itself.